Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics

Abstract

Abstract:To analyze and gain intuition on the mechanisms of complex systems of large dimensions, one strategy is to simplify the model by identifying a reduced system, in the form of a smaller set of variables and interactions that still capture specific properties of the system. For large models of biological networks, the diagram of interactions is often well represented by a Boolean model with a family of logical rules. The state space of a Boolean model is finite, and its asynchronous dynamics are fully described by a transition graph in the state space. In this context, a method will be developed for identifying the active or operational interactions responsible for a given dynamic behaviour. The first step in this procedure is the decomposition of the asynchronous transition graph into its strongly connected components, to obtain a "reduced" and hierarchically organized graph of transitions. The second step consists of the identification of a partial graph of interactions and a sub-family of logical rules that remain operational in a given region of the state space. This model reduction method and its usefulness are illustrated by an application to a model of programmed cell death. The method identifies two mechanisms used by the cell to respond to death-receptor stimulation and decide between the survival or apoptotic pathways. Key-words:

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

“…The control input u corresponds to the concentration level of the tumor necrosis factor (TNF, a stimulus). This model is introduced in [46], and is a simplified version of an apoptosis network model in [47]. In this model, x 2 (k) = 0 implies cell survival, and x 1 (k) = 0, x 2 (k) = 1 imply cell death.…”

Interconnection of asynchronous Boolean networks, asymptotic and transient dynamics

“…In principle, this graph can be fully analyzed using graph theoretical concepts and tools [23], and some classical algorithms [11], to describe transient and asymptotic behavior. The drawback is that such techniques become computationally prohibitive when the dimension increases, and hence the importance of using the knowledge of each separate module.…”

Predicting the asymptotic dynamics of large biological networks by interconnections of Boolean modules

“…Throughout this paper, we will consider asynchronous Boolean networks (ABN). The description and analysis of an ABN without inputs or outputs can be found in [9] (see also [10] and [11] for general references on graphs and positive matrices). For MIMO ABNs, the relevant objects can be defined as follows.…”

“…In contrast to [5], our interconnection method does not involve the projection onto a subset of variables, with the advantage that every variable of the original system is preserved. A further development of the method will be to extend the asymptotic graph to include (biological) transition probabilities (see for instance [3,9]), in order to compute the probability to reach each attractor from a given initial condition. This work is currently in progress.…”